Q: A 25-foot ladder leans against a house, forming a $$60^ ext{°}$$ angle with the ground. How tall is the house? Round your answer to the nearest 0.1 foot.

$$25 \times \sin(60^ ext{°}) = 21.7 ft$$

Q: A medical technician uses a $$30^ ext{°}$$ angle to position an X-ray machine. If the machine is 10 feet from the patient, what is the height above the ground where the X-ray beam hits the patient?

$$10 \times \sin(30^ ext{°}) = 5 ft$$

Question 1

A right triangle has legs $$a = 2$$ and $$b = 3. $$What is the exact value of $$\sin(A)$$, where $$A is $$the angle opposite side $$a$$? Express your answer with a rational denominator.

Accepted Answer

$$\sin(A) = \dfrac{2}{13}$$

Question 2

Convert $$60^	ext{°} to $$radians. Which of the following is correct?

Accepted Answer

$$\dfrac{\pi}{3}$$

Question 3

Convert $$\dfrac{5\pi}{6}$$ radians to degrees. Round your answer to the nearest degree.

Accepted Answer

$$150^	ext{°}$$

Question 4

Given $$\sin(	heta) = \dfrac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 5

If $$	an(	heta) = 2$$ and $$\sin(	heta) \u003e 0$$, what is $$\sin(	heta)$$?

Accepted Answer

$$\dfrac{2}{\sqrt{1 + 2^2$}} = \dfrac{2}{\sqrt{5}}$$

Question 6

The point $$(3, 4) is on $$the terminal side of angle $$	heta. $$What is $$\sin(	heta)$$?

Accepted Answer

$$\dfrac{4}{5}$$

Question 7

A 25-foot ladder leans against a house, forming a $$60^	ext{°}$$ angle with the ground. How tall is the house? Round your answer to the nearest 0.1 foot.

Accepted Answer

$$25 	imes \sin(60^	ext{°}) = 21.7 ft$$

Question 8

Which quadrant does the angle $$210^	ext{°}$$ lie in?

Accepted Answer

Quadrant III

Question 9

Determine the sign of $$\sin(-120^	ext{°}).$$

Accepted Answer

Negative

Question 10

Find the reference angle for $$-135^	ext{°}.$$

Accepted Answer

$$45^	ext{°}$$

Question 11

Use the reference angle to find the exact value of $$\sin(-135^	ext{°}).$$

Accepted Answer

$$-\dfrac{\sqrt{2}}{2}$$

Question 12

If $$\cos(	heta) = -\dfrac{3}{5}$$ and $$	heta is in $$Quadrant III, what is $$\sin(	heta)$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 13

If $$\sin(	heta) = \dfrac{1}{2}$$, what is $$	heta in $$degrees in the interval $$0 \u003c 	heta \u003c 180^	ext{°}$$?

Accepted Answer

$$30^	ext{°}$$ and $$150^	ext{°}$$

Question 14

Use the even-odd properties to find $$\cos(-	heta) if$$ $$\cos(	heta) = 0.6.$$

Accepted Answer

$$0.6$$

Question 15

Find the exact value of $$	an(225^	ext{°}).$$

Accepted Answer

$$-1$$

Question 16

What is the amplitude, period, and phase shift of $$y = -2\sin\left(x + \dfrac{\pi}{4}\right)$$?

Accepted Answer

Amplitude: $$2$$, Period: $$2\pi$$, Phase shift: $$\dfrac{\pi}{4} to $$the right

Question 17

A medical technician uses a $$30^	ext{°}$$ angle to position an X-ray machine. If the machine is 10 feet from the patient, what is the height above the ground where the X-ray beam hits the patient?

Accepted Answer

$$10 	imes \sin(30^	ext{°}) = 5 ft$$

Question 18

If $$	an(	heta) = -1$$ and $$	heta is in $$Quadrant IV, what is $$	heta in $$degrees?

Accepted Answer

$$315^	ext{°}$$

Question 19

A Ferris wheel rotates through an angle of $$\dfrac{\pi}{2}$$ radians. How many degrees is this?

Accepted Answer

$$90^	ext{°}$$

Question 20

If $$\sin(	heta) = -\dfrac{1}{2}$$ and $$	heta is $$between $$180^	ext{°}$$ and $$360^	ext{°}$$, what are the possible values for $$	heta$$?

Accepted Answer

$$210^	ext{°}$$ and $$330^	ext{°}$$

MA 15400 Trigonometry Review 1 – Step-by-Step Study Guidance

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